Some results on pseudo MV-algebras with square roots
Anatolij Dvure\v{c}enskij, Omid Zahiri

TL;DR
This paper explores the concept of square roots in pseudo MV-algebras, introducing various notions, classifying them, and characterizing their properties, especially in representable symmetric cases, with concrete examples.
Contribution
It introduces new notions of square roots in pseudo MV-algebras, classifies them, and characterizes their structure in representable symmetric cases using unital ℓ-groups.
Findings
Pseudo MV-algebras with square roots form a proper subvariety.
A strict square root classification is established.
Characterizations of square roots on representable symmetric pseudo MV-algebras are provided.
Abstract
The paper provides a study of pseudo MV-algebras with square roots. We introduce different notions of a square root on a pseudo MV-algebra, and present their main properties. We show that the class of pseudo-MV-algebras with square roots is a proper subvariety of the variety of pseudo MV-algebras. Then, we define a strict square root to classify the class of pseudo MV-algebras with square roots. We found a relationship between strongly atomless pseudo MV-algebras and strict pseudo MV-algebras. Finally, we investigate square roots on representable symmetric pseudo MV-algebras, and we present a complete characterization of a square root and a weak square root on a representable symmetric pseudo MV-algebra using addition in a unital -group. Some interesting examples are provided.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rough Sets and Fuzzy Logic
